Tsarnaev, 22, was convicted and sentenced last year to death in the 2013 attack. Two pressure cooker bombs placed near the marathon finish line by Tsarnaev and his brother killed three people and injured more than 260 others.

Tsarnaev also was convicted of killing a Massachusetts Institute of Technology police officer days later. During the sentencing hearing Tsarnaev admitted that he and his brother committed the bombings, and he apologized to the victims.

His brother, Tamerlan Tsarnaev, 26, died days after the bombing following a gunbattle with police.

The judge, in his order denying Dzhokhar Tsarnaev a new trial, noted that he and a federal appeals court had previously rejected arguments from Tsarnaev’s lawyers that he could not receive a fair trial in Boston, where many people knew the victims or had connections to the marathon. The defence also cited intense and continuing local news coverage of the victims and the anniversary of the bombings.

But the judge said the victims, the trial and other marathon-related events also were covered widely by national and international news organizations.

“There is no reason to think – and certainly no specific evidence – that this extensive coverage would have been any different in kind or degree if the trial had been conducted elsewhere,” he wrote in his order. “This was not a crime that was unknown outside of Boston.”

The judge also rejected Tsarnaev’s renewed challenge to the constitutionality of the federal death penalty. Tsarnaev’s lawyers cited a dissenting opinion in a U.S. Supreme Court ruling last year by Justice Stephen Breyer and Justice Ruth Bader Ginsburg, who said they think it’s “highly likely” the death penalty is unconstitutional. But the judge in Tsarnaev’s case said that whatever the merits of the dissent, the majority opinion was the binding precedent.